Sparse Support Vector Machine with <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> Penalty for Feature Selection

We study the strategies in feature selection with sparse support vector machine (SVM). Recently, the socalled L _p -SVM (0 < p < 1) has attracted much attention because it can encourage better sparsity than the widely used L ₁-SVM. However, L _p -SVM is a non-convex and non-Lipschitz optimization problem. Solving this problem numerically is challenging. In this paper, we reformulate the L _p -SVM into an optimization model with linear objective function and smooth constraints (LOSC-SVM) so that it can be solved by numerical methods for smooth constrained optimization. Our numerical experiments on artificial datasets show that LOSC-SVM (0 < p < 1) can improve the classification performance in both feature selection and classification by choosing a suitable parameter p. We also apply it to some real-life datasets and experimental results show that it is superior to L ₁-SVM.     

Efficient <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript> norm based sparse subspace clustering via smooth IRLS and ADMM

Recently, sparse subspace clustering, as a subspace learning technique, has been successfully applied to several computer vision applications, e.g. face clustering and motion segmentation. The main idea of sparse subspace clustering is to learn an effective sparse representation that are used to construct an affinity matrix for spectral clustering. While most of existing sparse subspace clustering algorithms and its extensions seek the forms of convex relaxation, the use of non-convex and non-smooth l _q (0 < q < 1) norm has demonstrated better recovery performance. In this paper we propose an l _q norm based Sparse Subspace Clustering method (lqSSC), which is motivated by the recent work that l _q norm can enhance the sparsity and make better approximation to l ₀ than l ₁. However, the optimization of l _q norm with multiple constraints is much difficult. To solve this non-convex problem, we make use of the Alternating Direction Method of Multipliers (ADMM) for solving the l _q norm optimization, updating the variables in an alternating minimization way. ADMM splits the unconstrained optimization into multiple terms, such that the l _q norm term can be solved via Smooth Iterative Reweighted Least Square (SIRLS), which converges with guarantee. Different from traditional IRLS algorithms, the proposed algorithm is based on gradient descent with adaptive weight, making it well suit for general sparse subspace clustering problem. Experiments on computer vision tasks (synthetic data, face clustering and motion segmentation) demonstrate that the proposed approach achieves considerable improvement of clustering accuracy than the convex based subspace clustering methods.     

基于Gabor特征和支持向量引导字典学习的人脸识别

稀疏编码中的字典学习在稀疏表示的图像识别中扮演着重要的作用。由于Gabor特征对表情、光照和姿态等变化具有一定的鲁棒性,提出一种基于Gabor特征和支持向量引导字典学习（GSVGDL）的稀疏表示人脸识别算法。先提取图像的Gabor特征,然后用增广Gabor特征矩阵来构造初始字典。字典学习模型中综合了重构误差项、判别项和正则化项,判别项公式化定义为所有编码向量对平方距离的加权总和;通过字典学习同时得到字典原子与类别标签相对应的结构化字典和线性分类器。该字典学习方法能够自适应地为不同的编码向量对分配不同的权值,提高了字典的判别性能。实验结果表明该方法具有很好的识别精度和较高的识别效率。     

基于Gabor特征与加权协同表示的人脸识别算法

针对基于稀疏表示分类方法的训练样本于与类别标签信息提取不足,特别是在训练样本和待测样本都受到噪声污染的情况下将会明显下降及算法复杂度较高的问题,提出以Gabor特征以及加权协同为基础的人脸识别算法;最初需要对人脸图像内所包含的各个尺度以及方向的Gabor特征完成提取,在稀疏表示中引入Gabor特征,将降维后的Gabor特征矩阵作为超完备字典,再用稀疏表示增强加权协同表示得到该字典下的的稀疏表示系数,然后利用增强系数与训练样本的标签矩阵完成对测试样本进行分类识别,从而得到Gabor特征以及加权的协同表示分类方法,在Yale人脸数据库、Extended Yale B和AR人脸数据库上以及在FERET人脸数据库对人脸姿态变化的实验表明新算法具有更好的识别率和较短的计算时间.     

Discriminative sparse representation for face recognition

Recently Sparse Representation (or coding) based Classification (SRC) has gained great success in face recognition. In SRC, the testing image is expected to be best represented as a sparse linear combination of training images from the same class, and the representation fidelity is measured by the ?₂-norm or ?₁-norm of the coding residual. However, SRC emphasizes the sparsity too much and overlooks the spatial information during local feature encoding process which has been demonstrated to be critical in real-world face recognition problems. Besides, some work considers the spatial information but overlooks the different discriminative ability in different face regions. In this paper, we propose to weight spatial locations based on their discriminative abilities in sparse coding for robust face recognition. Specifically, we learn the weights at face locations according to the information entropy in each face region, so as to highlight locations in face images that are important for classification. Furthermore, in order to construct a robust weights to fully exploit structure information of each face region, we employed external data to learn the weights, which can cover all possible face image variants of different persons, so the robustness of obtained weights can be guaranteed. Finally, we consider the group structure of training images (i.e. those from the same subject) and added an ?_2,1-norm (group Lasso) constraint upon the formulation, which enforcing the sparsity at the group level. Extensive experiments on three benchmark face datasets demonstrate that our proposed method is much more robust and effective than baseline methods in dealing with face occlusion, corruption, lighting and expression changes, etc.     

自适应加权特征字典与联合稀疏相结合的遥感目标检测

随着分辨率的提高,遥感图像空间包含的有用信息越来越丰富,这使得遥感数据的处理变得更加复杂,容易发生维数灾难并影响识别效果。针对这一情况,提出一种自适应加权特征字典与联合稀疏相结合的遥感图像目标检测方法(GJ-SRC)。首先将训练图像和待测图像进行Gabor变换以提取特征图像。然后计算各个特征值在进行稀疏表示时的贡献权重,通过自适应方法构造特征字典,使字典具有更强的判别能力。最后,提取每一类图像的公共特征和单个图像的私有特征构成联合字典,并利用测试图像稀疏表示进行目标检测识别。为了避免Gabor变换产生的维数灾难,在处理过程中采用PCA方法对特征字典进行降维,以降低计算成本。实验表明,与现有的SRC方法和遥感目标检测方法等相比,所提方法具有较好的检测效果。     

Robust face recognition via occlusion dictionary learning

Sparse representation based classification (SRC) has recently been proposed for robust face recognition. To deal with occlusion, SRC introduces an identity matrix as an occlusion dictionary on the assumption that the occlusion has sparse representation in this dictionary. However, the results show that SRC's use of this occlusion dictionary is not nearly as robust to large occlusion as it is to random pixel corruption. In addition, the identity matrix renders the expanded dictionary large, which results in expensive computation. In this paper, we present a novel method, namely structured sparse representation based classification (SSRC), for face recognition with occlusion. A novel structured dictionary learning method is proposed to learn an occlusion dictionary from the data instead of an identity matrix. Specifically, a mutual incoherence of dictionaries regularization term is incorporated into the dictionary learning objective function which encourages the occlusion dictionary to be as independent as possible of the training sample dictionary. So that the occlusion can then be sparsely represented by the linear combination of the atoms from the learned occlusion dictionary and effectively separated from the occluded face image. The classification can thus be efficiently carried out on the recovered non-occluded face images and the size of the expanded dictionary is also much smaller than that used in SRC. The extensive experiments demonstrate that the proposed method achieves better results than the existing sparse representation based face recognition methods, especially in dealing with large region contiguous occlusion and severe illumination variation, while the computational cost is much lower.     

Laplacian sparse dictionary learning for image classification based on sparse representation

Sparse representation is a mathematical model for data representation that has proved to be a powerful tool for solving problems in various fields such as pattern recognition, machine learning, and computer vision. As one of the building blocks of the sparse representation method, dictionary learning plays an important role in the minimization of the reconstruction error between the original signal and its sparse representation in the space of the learned dictionary. Although using training samples directly as dictionary bases can achieve good performance, the main drawback of this method is that it may result in a very large and inefficient dictionary due to noisy training instances. To obtain a smaller and more representative dictionary, in this paper, we propose an approach called Laplacian sparse dictionary (LSD) learning. Our method is based on manifold learning and double sparsity. We incorporate the Laplacian weighted graph in the sparse representation model and impose the l₁-norm sparsity on the dictionary. An LSD is a sparse overcomplete dictionary that can preserve the intrinsic structure of the data and learn a smaller dictionary for each class. The learned LSD can be easily integrated into a classification framework based on sparse representation. We compare the proposed method with other methods using three benchmark-controlled face image databases, Extended Yale B, ORL, and AR, and one uncontrolled person image dataset, i-LIDS-MA. Results show the advantages of the proposed LSD algorithm over state-of-the-art sparse representation based classification methods.     

联合Gabor误差字典和低秩表示的人脸识别算法

针对人脸图片的遮挡、伪装、光照及表情变化等问题,根据Gabor特征对遮挡、伪装、光照及表情变化有着更强的鲁棒性的特点,提出了联合Gabor误差字典和低秩表示的人脸识别算法(GDLRR)。首先对训练样本和测试样本分别进行Gabor特征提取,并将这些特征组成待测试的特征字典;然后将一个单位阵进行Gabor特征提取并训练成一个更紧凑的Gabor误差字典;最后联合Gabor误差字典和训练特征字典对测试特征字典进行低秩表示后进行分类识别。各类实验表明,提出的改进算法对人脸识别的各类问题都有着更强的鲁棒性和更高的识别准确率。     

Positive <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>-gain filter design for positive continuous-time Markovian jump systems with partly known transition rates

The paper is concerned with the problem of positive L ₁-gain filter design for positive continuous-time Markovian jump systems with partly known transition rates. Our aim is to design a positive full-order filter such that the corresponding filtering error system is positive and stochastically stable with L ₁-gain performance. By applying a linear co-positive Lyapunov function and free-connection weighting vectors, the desired positive L ₁-gain filter is provided. The obtained theoretical results are demonstrated by numerical examples.     

改进稀疏表示算法在人脸识别中的应用

人脸识别的主要难度在于，受到光照变化、表情变化以及遮挡的影响，会使得采集的不同人的人脸图像具有相似性。为有效解决基于稀疏表示的分类算法（Sparse Representation-based Classification，SRC）在人脸训练样本不足时会导致识别率降低和稀疏表示求解效率较低的问题，提出了基于判别性低秩分解与快速稀疏表示分类（Low Rank Recovery Fast Sparse Representation-based Classification，LRR_FSRC）的人脸识别算法。利用低秩分解理论得到低秩恢复字典以及稀疏误差字典，结合低秩分解和结构不相干理论，训练出判别性低秩类字典和稀疏误差字典，并把它们结合作为测试时所用的字典；用坐标下降法来求解稀疏系数以提高了计算效率；根据重构误差实现测试样本的分类。在YALE和ORL数据库上的实验结果表明，提出的基于LRR_FSRC的人脸识别方法具有较高的识别率和计算效率。     

On Supersymmetric M-brane configurations with an R<Stack><Subscript>*</Subscript><Superscript>1,1</Superscript></Stack> /Z<Subscript>2</Subscript> submanifold

We obtain new examples of partly supersymmetric M-brane solutions defined on products of Ricci-flat manifolds, which contain a two-dimensional Lorentzian submanifold R _* ^1,1 /Z ₂ with one parallel spinor. The examples belong to the following configurations: M2, M5, M2 ∩M5 and M5 ∩M5. Among them, an M2 solution with N = 1/32 fractional number of preserved supersymmetries is presented.     

<Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>-Optimal Nonparametric Frontier Estimation via Linear Programming

A frontier estimation method for a set of points on a plane is proposed, being optimal in L₁-norm on a given class of β-Holder boundary functions under β ∈ (0, 1]. The estimator is defined as sufficiently regular linear combination of kernel functions centered in the sample points, which covers all these points and whose associated support is of minimal surface. The linear combination weights are calculated via solution of the related linear programming problem. The L₁-norm of the estimation error is demonstrated to be convergent to zero with probability one, with the optimal rate of convergence.     

自适应Gabor特征的协同表示人脸识别算法

为了解决人脸识别应用中针对人脸姿态的变化,光照等外部环境变化导致识别率不高,且稀疏表示应用于人脸识别收敛速度慢的情况,提出了一种基于多分量的Gabor特征提取和自适应权重选择的协同表示人脸识别算法(GAW-CRC).特征提取阶段,将Gabor变换的所有特征分量中鉴别能力较差的分量淘汰,剩余分量构建特征字典,分别协同表示对应测试样本的特征分量,将所有剩余分量的识别结果,按照自适应的权重函数加权融合得出最终分类结果.实验证明:算法应用于AR,FERET与Extended Yale B人脸库中,当对应的样本存在人脸角度变化,表情变化和光照条件变化等情况时,能够得到更高的识别率.     

基于Gabor小波和稀疏表示的人脸表情识别

通过分析Gabor小波和稀疏表示的生物学背景和数学特性,提出一种基于Gabor小波和稀疏表示的人脸表情识别方法。采用Gabor小波变换对表情图像进行特征提取,建立训练样本Gabor特征的超完备字典,通过稀疏表示模型优化人脸表情图像的特征向量,利用融合识别方法进行多分类器融合识别分类。实验结果表明,该方法能够有效提取表情图像的特征信息,提高表情识别率。     

Collaborative representation analysis methods for feature extraction

Recently, sparse representation (SR) theory gets much success in the fields of pattern recognition and machine learning. Many researchers use SR to design classification methods and dictionary learning via reconstruction residual. It was shown that collaborative representation (CR) is the key part in sparse representation-based classification (SRC) and collaborative representation-based classification (CRC). Both SRC and CRC are good classification methods. Here, we give a collaborative representation analysis (CRA) method for feature extraction. Not like SRC-/CRC-based methods (e.g., SPP and CRP), CRA could directly extract the features like PCA and LDA. Further, a Kernel CRA (KCRA) is developed via kernel tricks. The experimental results on FERET and AR face databases show that CRA and KCRA are two effective feature extraction methods and could get good performance.

     

<Emphasis Type="Italic">I</Emphasis><Subscript>DDT</Subscript>: Fundamentals and test generation

It is the time to explore the fundamentals ofI _DDT testing when extensive work has been done forI _DDT testing since it was proposed. This paper precisely defines the concept of average transient current (I _DDT) of CMOS digital ICs, and experimentally analyzes the feasibility ofI _DDT test generation at gate level. Based on the SPICE simulation results, the paper suggests a formula to calculateI _DDT by means of counting only logical up-transitions, which enablesI _DDT test generation at logic level. The Bayesian optimization algorithm is utilized forI _DDT test generation. Experimental results show that about 25% stuck-open faults are withI _DDT test generation. 2.5, and likely to beI _DDT testable. It is also found that mostI _DDT testable faults are located near the primary inputs of a circuit under test.I _DDT test generation does not require fault sensitization procedure compared with stuck-at fault test generation. Furthermore, some redundant stuck-at faults can be detected by usingI _DDT testing.     

基于多尺度稀疏表示的面部疲劳识别

针对疲劳驾驶严重威胁道路交通安全的问题,提出了一种基于多尺度稀疏表示的面部疲劳识别算法。该算法首先通过Gabor小波获取面部多尺度多方向的疲劳特征;然后采用2D-PCA方法对提取的特征进行降维处理,提高算法的执行效率;最后通过稀疏表示的方法构造疲劳的超完备字典并完成疲劳识别。实验在自建的疲劳数据库中完成,结果显示所提算法的疲劳识别率达到94.5%,具有一定的可行性。     

基于非凸低秩分解判别的叠加线性稀疏人脸识别

目的 针对因采集的人脸图像样本受到污染而严重干扰人脸识别及训练样本较少（小样本）时会由于错误的稀疏系数导致性能急剧下降从而影响人脸识别的问题,提出了一种基于判别性非凸低秩矩阵分解的叠加线性稀疏表示算法。方法 首先由γ范数取代传统核范数,克服了传统低秩矩阵分解方法求解核范数时因矩阵奇异值倍数缩放导致的识别误差问题;然后引入结构不相干判别项,以增加不同类低秩字典间的非相干性,达到抑制类内变化和去除类间相关性的目的;最后利用叠加线性稀疏表示方法完成分类。结果 所提算法在AR人脸库中的识别率达到了98.67±0.57%,高于SRC（sparse representation-based classification）、ESRC（extended SRC）、RPCA（robust principal component analysis）+SRC、LRSI（low rank matrix decomposition with structural incoherence）、SLRC（superposed linear representation based classification）-l₁等算法;同时,遮挡实验表明,算法对遮挡图像具有更好的鲁棒性,在不同遮挡比例下,相比其他算法均有更高的识别率。在CMU PIE人脸库中,对无遮挡图像添加0、10%、20%、30%、40%的椒盐噪声,算法识别率分别达到90.1%、85.5%、77.8%、65.3%和46.1%,均高于其他算法。结论 不同人脸库、不同比例遮挡和噪声的实验结果表明,所提算法针对人脸遮挡、表情和光照等噪声因素依然保持较高的识别率,鲁棒性更好。     

基于稀疏表示与小波特征的人脸识别分层框架

基于稀疏表示的人脸识别研究,非线性特征的选择研究较少。提出分层使用人脸图像的小波特征,进行稀疏表示人脸识别框架。框架首先对样本人脸进行小波变换,构造小波低频和小波高频过完备人脸字典;识别阶段首先使用人脸图像的小波低频特征进行稀疏表示,计算类别模糊稀疏,然后根据模糊系数输出类别标签或进行高频特征的稀疏表示与识别。实验结果表明,基于小波特征和稀疏表示的人脸识别分层框架提高了识别的准确率,且对遮挡很鲁棒。